@article {13242, title = {Ranks and presentations of some normally ordered inverse semigroups}, journal = {Periodica Mathematica Hungarica (DOI 10.1007/s10998-022-00448-8)}, volume = { 85}, year = {2022}, pages = {435{\textendash}447}, abstract = {

In this paper we compute the rank and exhibit a presentation for the monoids
of all $P$-stable and $P$-order preserving partial permutations on a finite set
$\Omega$, with $P$ an ordered uniform partition of $\Omega$. These (inverse)
semigroups constitute a natural class of generators of the pseudovariety of
inverse semigroups ${\sf NO}$ of all normally ordered (finite) inverse
semigroups.

}, url = {https://doi.org/10.1007/s10998-022-00448-8}, author = {Caneco, Rita and Fernandes, V{\'\i}tor H. and Quinteiro, Teresa M.} }